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Proof step 35 from proof validrefs-delcycle-01 (previous step)

validrefs(str, (r0 ' + acc) + r ' + refs0 + r ' + refs1, ty, st), is_valid_ref(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str, r, refs0, refs1, ty, st. validrefs(str, acc + r ' + refs0 + r ' + refs1, ty, st) → validrefs(str, acc + r ' + refs1, ty, st) ⊦ r0 = jvmref, validrefs(str, (r0 ' + acc) + r ' + refs1, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st)
Proof step 34:
validrefs(str, (r0 ' + acc) + r ' + refs0 + r ' + refs1, ty, st), is_obj(str, r0, st) ∨ is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str, r, refs0, refs1, ty, st. validrefs(str, acc + r ' + refs0 + r ' + refs1, ty, st) → validrefs(str, acc + r ' + refs1, ty, st) ⊦ r0 = jvmref, validrefs(str, (r0 ' + acc) + r ' + refs1, ty, st)

Rule argument

[speclemmaarg: ,is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st) ,[st, r, str] → [st, r0, str] ,F ,addfuns , ,is-valid-ref-stronger-def ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r0, str)]]